Factorial Randomized Complete Block Design analysis

I am trying to do RCBD factorial analysis using 'doebioresearch' package. The anova is showing that the interaction effect is not significant. However, when compared the mean using Least Significance Test it is giving the different letters for the interaction (Cd*Si). Could you please explain why this is happening? Thanks a lot for helping. Below is the reprex:

mydata= data.frame(
  stringsAsFactors = FALSE,
  Replication = c(1L,1L,1L,1L,1L,
                  1L,1L,1L,1L,2L,2L,2L,2L,
                  2L,2L,2L,2L,2L,3L,3L,3L,3L,
                  3L,3L,3L,3L,3L),
  Cd = c("Cd0","Cd0","Cd0",
         "Cd10","Cd10","Cd10","Cd20",
         "Cd20","Cd20","Cd0","Cd0",
         "Cd0","Cd10","Cd10","Cd10","Cd20",
         "Cd20","Cd20","Cd0","Cd0",
         "Cd0","Cd10","Cd10","Cd10","Cd20",
         "Cd20","Cd20"),
  Si = c("SiNP0","SiNP0.5",
         "SiNP1","SiNP0","SiNP0.5",
         "SiNP1","SiNP0","SiNP0.5","SiNP1",
         "SiNP0","SiNP0.5","SiNP1",
         "SiNP0","SiNP0.5","SiNP1","SiNP0",
         "SiNP0.5","SiNP1","SiNP0",
         "SiNP0.5","SiNP1","SiNP0","SiNP0.5",
         "SiNP1","SiNP0","SiNP0.5",
         "SiNP1"),
  Dry.wt = c(7.77,8.67,9.57,
             5.64,6.97,8.73,2.53,5.79,6.9,
             6.19,7.83,8.24,5.76,6.13,7.04,
             3.78,5.44,6.25,7.46,8.21,
             8.86,5.64,6.72,7.78,3.95,6.84,
             6.95)
)
mydata
#>    Replication   Cd      Si Dry.wt
#> 1            1  Cd0   SiNP0   7.77
#> 2            1  Cd0 SiNP0.5   8.67
#> 3            1  Cd0   SiNP1   9.57
#> 4            1 Cd10   SiNP0   5.64
#> 5            1 Cd10 SiNP0.5   6.97
#> 6            1 Cd10   SiNP1   8.73
#> 7            1 Cd20   SiNP0   2.53
#> 8            1 Cd20 SiNP0.5   5.79
#> 9            1 Cd20   SiNP1   6.90
#> 10           2  Cd0   SiNP0   6.19
#> 11           2  Cd0 SiNP0.5   7.83
#> 12           2  Cd0   SiNP1   8.24
#> 13           2 Cd10   SiNP0   5.76
#> 14           2 Cd10 SiNP0.5   6.13
#> 15           2 Cd10   SiNP1   7.04
#> 16           2 Cd20   SiNP0   3.78
#> 17           2 Cd20 SiNP0.5   5.44
#> 18           2 Cd20   SiNP1   6.25
#> 19           3  Cd0   SiNP0   7.46
#> 20           3  Cd0 SiNP0.5   8.21
#> 21           3  Cd0   SiNP1   8.86
#> 22           3 Cd10   SiNP0   5.64
#> 23           3 Cd10 SiNP0.5   6.72
#> 24           3 Cd10   SiNP1   7.78
#> 25           3 Cd20   SiNP0   3.95
#> 26           3 Cd20 SiNP0.5   6.84
#> 27           3 Cd20   SiNP1   6.95
attach(mydata)
library(doebioresearch)
RCBD2FLSD<-frbd2fact(mydata[4], Replication, Cd, Si, 1)
RCBD2FLSD

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